A few years ago, British-German relations seemed to be of merely historical interest. In so far as there were disagreements between the governments of the two countries, they were mostly about how the European Union should deal with the rest of the world. By the end of the 2000s, even the British tabloids seemed to have put the fiercely anti-German headlines of the mid-90s behind them.

However, the euro crisis has reopened wounds that seemed until then to have healed. The mutual incomprehension between the two countries came to a head at the European summit last December when David Cameron vetoed Angela Merkel's plan for "fiscal union" after she refused to give him what seemed to her unreasonable guarantees to protect the City. The future of the EU will be determined to a large extent by the increasingly fraught relationship between Germany and the UK – the most powerful eurozone country and the leading euro-out.

This estrangement gives Keeping Up with the Germans a somewhat harder edge than it might otherwise have had. Philip Oltermann deftly intersperses his own experience of Britain with other "encounters" between Britons and Germans – Margaret Thatcher and Helmut Kohl, William Cobbett and Heinrich Heine, AJ Ayer and Theodor Adorno, and so on – to explore the different attitudes of the two countries to everything from language and politics to sex and sport.

Oltermann grew up in Hamburg and moved to Britain at the age of 16 in 1996 – when relations between Britain and Germany were at a low – after his father got a job in London. Although he is baffled by many aspects of British life and initially struggles with the English language and British food, Phil the German gradually becomes an Anglophile who listens to Britpop and mimics the insouciance and irony of his teenage British counterparts.

Oltermann subtly explores the fluidity of national stereotypes. For example, he juxtaposes the German Romantic writer Jean Paul's perception of Britain as a country obsessed by machines at a time when the country was about to become the workshop of the world with Kraftwerk's album The Man-Machine – released in 1978 at a time when British manufacturing was in terminal decline.

For most of the book, Oltermann avoids the second world war, which he sees as a "black hole". (Of all the characters in the book he discusses at any length, the closest to a Nazi is Unity Mitford.) But eventually he realises he cannot altogether avoid the Nazi past, which is not just a British obsession but also a German one without which it is impossible to understand the postwar Federal Republic.

For example, the young West Germans who took to the streets in 1968 were protesting not just about the Vietnam war but also about the perceived continuities between the Third Reich and the Federal Republic. "You had all these professors, judges and chiefs of police who were old Nazis and you had to get rid of them, and a certain violence was necessary to clear up the mess," the poet Hans Magnus Enzensberger tells Oltermann.

This violence culminated in the leftwing terrorism of the 1970s: Oltermann neatly contrasts West Germans like Astrid Proll of the Red Army Faction who embarked on an armed struggle against the state and Brits like Joe Strummer of the Clash who literally just wore the T-shirt.

At the same time, however, mainstream West Germany was becoming more liberal. This seems to Oltermann to suggest that countries can change and undergo the "revolution of the mind" that Martha Gellhorn said Germany needed in 1964. Yet he also worries that Germany's slightly obsessive environmentalism – illustrated by its reaction to the Fukushima nuclear disaster last year – is influenced by romanticism and suggests that "deep flaws in the national psyche had survived".

Olterman sees Britain as a country that has also changed dramatically (unlike most German commentators, who see it as "an island set in aspic"). In fact, antipathy towards Germany has generally been replaced by apathy – at least until recently.

He concludes optimistically, if not entirely convincingly, that a "gradual rapprochement… is taking place beneath the surface". Exasperated by Germany's response to the euro crisis, even the Guardian – not exactly an anti-German newspaper – recently wrote in a leader of German "fiscal imperialism". Rather than converging, we may actually be growing further apart as Germany becomes more dominant and Britain more Eurosceptic.